Smallest event horizon for a black hole?

[Chronos]

Quoth wolfpup:

Right, on the gravity question, microscopic black holes by definition have an event horizon and a singularity at the center, so their gravitational strength at the EV is exactly that of massive black holes, and the theoretical density at the singularity infinite, or else they wouldn’t be black holes at all! The only difference between supermassive black holes and tiny microscopic ones is the gravitational gradient.

(I’m assuming that “EV” means “Event horizon”)
That depends on what you mean by “gravitational strength”. If you mean the gravitational potential, then yes, that’s going to be the same for a black hole of any size. Usually, though, I would interpret “gravitational strength” to mean the magnitude of the gravitational field, or possibly the magnitude of the curvature, and either of those is going to be much greater for a small black hole than for a large one.

And the details of what “really happens” in Hawking radiation aren’t really accessible knowledge. All we can say is that particles leave the vicinity of the black hole, and that the mass of the black hole decreases as a result. It quacks like particles leaving the hole. The descriptions used to set up the calculations might not frame them that way, but those are just calculational tools, and do not necessarily reflect “reality” (whatever that is).

[wolfpup]

@Chronos

(I’m assuming that “EV” means “Event horizon”)
That depends on what you mean by “gravitational strength”. If you mean the gravitational potential, then yes, that’s going to be the same for a black hole of any size. Usually, though, I would interpret “gravitational strength” to mean the magnitude of the gravitational field, or possibly the magnitude of the curvature, and either of those is going to be much greater for a small black hole than for a large one.

Sorry, yes, I meant “event horizon” (henceforth “EH)”. I guess for some reason “electric vehicle” stuck in my brain!

What I specifically meant by “gravitational strength” is “gravitational force” – as in F=ma – which will be exactly the same at the EH of an arbitrarily tiny black hole as it would be at the EH of a supermassive one. I was trying to counter the incorrect supposition that smaller black holes evaporate more quickly because “they don’t have enough gravity”, which is not the correct interpretation.

@Chronos

And the details of what “really happens” in Hawking radiation aren’t really accessible knowledge. All we can say is that particles leave the vicinity of the black hole, and that the mass of the black hole decreases as a result. It quacks like particles leaving the hole. The descriptions used to set up the calculations might not frame them that way, but those are just calculational tools, and do not necessarily reflect “reality” (whatever that is).

That’s a good and interesting point. David Deutsch would have some interesting comments about that distinction between mathematics and philosophy.

[buddy431]

@Chronos

(I’m assuming that “EV” means “Event horizon”)
That depends on what you mean by “gravitational strength”. If you mean the gravitational potential, then yes, that’s going to be the same for a black hole of any size. Usually, though, I would interpret “gravitational strength” to mean the magnitude of the gravitational field, or possibly the magnitude of the curvature, and either of those is going to be much greater for a small black hole than for a large one.

And the details of what “really happens” in Hawking radiation aren’t really accessible knowledge. All we can say is that particles leave the vicinity of the black hole, and that the mass of the black hole decreases as a result. It quacks like particles leaving the hole. The descriptions used to set up the calculations might not frame them that way, but those are just calculational tools, and do not necessarily reflect “reality” (whatever that is).

Note too the Hawking radiation has never been observed. It’s something that most physicists think ought to happen, but realize that black holes represent an extreme condition and we’re not always exactly sure how our physical laws, as we understand them, apply such a strange object.

[Chronos]

Gravitational force (for a test particle of a given mass) is the gravitational field, and is one of the things I mentioned as being larger for a smaller hole. Consider that it scales as M/r^2, and that for a black hole, r is proportional to M. And in fact, the temperature of a black hole is exactly proportional to its surface gravity (even for cases like a rotating or charged black hole), so one could truthfully say that smaller black holes evaporate quicker because they have too much gravity.